Respuesta :
Answer: { (1,3), (2,1), (3,-1) }
Explanation
We start with the inner function f(x).
A function is basically a collection of (x,y) points. Often you'll see the points connected with a line or curve of some kind. However in this case, the points are separate disconnected islands.
For function f(x), the input x = 1 leads to output y = f(x) = 2. This is due to the point (1,2) inside f(x). We say that f(1) = 2.
This will mean g( f(x) ) = g( f(1) ) = g(2) = 3.
The g(2) = 3 is because (2,3) is inside g(x).
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To rephrase the last section:
x = 1 leads to f(1) = 2 and leads to g(2) = 3
Therefore g( f(x) ) = 3 when x = 1. In other words g( f(1) ) = 3.
Therefore (1,3) is a point in the g(f(x)) function.
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Follow the same type of logic to determine that x = 2 leads to f(2) = 3 and g(3) = 1. Therefore (2,1) is also a point in the g(f(x)) function.
If x = 3 then f(3) = 5 and g(5) = -1. Therefore (3,-1) is another point in the answer.
Now onto x = 4. We see that f(4) = 7 and g(7) = undefined. The undefined is due to none of the g(x) points having x = 7. Since the final result is undefined we ignore the input x = 4. Note how x = 7 is not in the domain of g(x).
Lastly x = 5. We see that f(5) = 9 and g(9) = undefined. We'll ignore x = 5 as well. The x = 9 isn't in the domain of g(x).
Ultimately the following points are inside g(f(x)):
(1,3), (2,1), (3,-1)
Separate each ordered pair with a comma. Surround the collection of points in curly braces to indicate we have a set.
